Westley, 45, guided Boro to promotion to the Football League in 2010 and into League One the following year and is poised to replace Smith after he was sacked last week.
Following his success at Stevenage, Westley quit to join Preston in January last year but was axed last month with the club just five points above the relegation zone.
Boro say they have a shortlist of three potential new managers but Westley is in pole position and could be back in charge at Broadhall Way over the weekend.
Chairman Phil Wallace said: "Yes, of course Graham is in the frame, along with several others.
"His past achievements for the club would put him in a good position and I'm long over the events of a year ago.
"I always understood the opportunity he had and his reasons for wanting to leave, I just didn't agree with the timing but that's history.
"We have a shortlist now of three and I'd hope that we can make an appointment over the weekend."